[(1-log6底3)^2+log6底2*log6底18]÷log6底4=

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[(1-log6底3)^2+log6底2*log6底18]÷log6底4=

[(1-log6底3)^2+log6底2*log6底18]÷log6底4=
[(1-log6底3)^2+log6底2*log6底18]÷log6底4=

[(1-log6底3)^2+log6底2*log6底18]÷log6底4=
原式={[log6(6)-log6(3)]²+log6(2)*log6(18)]÷log6(4)
={[log6(6÷3)]²+log6(2)*log6(18)}÷log6(4)
={[log6(2)]²+log6(2)*log6(18)}÷log6(4)
={log6(2)*[log6(2)+log6(18)]}÷log6(4)
=log6(2)*[log6(2×18)]÷log6(4)
=log6(2)*[log6(6²)]÷log6(4)
换底公式
=(lg2/lg6)*2÷(lg4/lg6)
=2lg2÷lg4
=2lg2÷2lg2
=1